Mandl and a colleague analyzed the insurance records of more than 700,000 women from 2011 to 2013. The women were between the ages of 40 and 59, and they all had routine mammograms to screen for breast cancer during that time period.

About 11 percent of the women had "suspicious" mammograms and were subjected to further testing, including repeat mammograms, ultrasounds and needle biopsies. For nearly all these women — 98.6 percent — cancer was not confirmed in further testing.

When Mandl projects this percentage of false alarms to the entire female population over age 40, he estimates that the U.S. spends $2.8 billion dollars each year on follow-up tests for suspicious results that turn out not to be cancer.

And even when cancer is detected, some of those tumors might be of low-risk to the patient — slow-growing and not likely to become invasive or life-threatening. But once suspicions are raised, Mandl says, overtreatment is often the result. "Overtreatment is bad," he says. "That's mastectomy, chemotherapy, radiation, in women who may not have needed any medical treatment at all."

For example, patients diagnosed with ductal carcinoma in situ can face radiation, chemotherapy and even mastectomy despite the fact that the cancer is noninvasive.

Mandl estimates that the cost of overtreatment adds up to $1.2 billion each year, resulting in a grand total of $4 billion in unnecessary spending annually.

And it's not just the financial cost that's a problem. When a woman receives a suspicious mammogram result, it often creates psychological stress and anxiety, Mandl says.

Still, some researchers have issues with Mandl's findings. Dr. Richard Wender, of the American Cancer Society, says the study overestimates the cost of unnecessary testing and incorrect diagnoses. And he says it fails to consider the proven benefits of annual mammograms.

"Mammograms are the most effective way we have to find breast cancer before anybody can feel it, before you're aware of it," Wender says.

He points to studies showing that mammograms reduce the risk of dying from breast cancer by 20 percent. "So whenever we're doing decision making, either as policy makers or just between one woman and her doctors, it's critical to look at ... benefits as well as downsides," he says.

Harvard's Mandl would like to reduce the number of screening mammograms even further. He suggests that screening be based on a woman's overall risk factors for breast cancer, including family history, obesity and breast density, as well as age.

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DAVID GREENE, HOST:

Mammograms, which can detect cancer early, can also raise red flags that turn out to be nothing. And as NPR's Patti Neighmond reports, new research puts a price tag on these false alarms.

NEIGHMOND: That's right, $4 billion a year on inaccurate results of mammograms. Mandl's a professor at Harvard Medical School. He reviewed medical records of more than 702,000 women between the ages of 40 and 59 who received routine screening mammograms in 2012. One in 10 of those women were told there were suspicious shadows on their mammogram x-rays.

MANDL: Those shadows are certain shapes and patterns. And densities of those shadows are associated with tumors.

NEIGHMOND: The important word here is associated. It turned out 98.6 percent of those women did not have cancer, but to figure that out takes more tests - repeat mammograms, ultrasound, needle biopsies. And even when cancer is detected, sometimes it can be low-risk, slow-growing tumors that aren't likely to become invasive or life-threatening. But once suspicions are raised, Mandl says, it often leads to overtreatment.

MANDL: Mastectomy, chemotherapy, radiation in women who may not have needed any medical treatment at all.

NEIGHMOND: But other experts feel strongly about the benefit of routine mammograms. Dr. Richard Wender heads the cancer prevention program at the American Cancer Society. He says the study overestimates the cost of additional testing, and it doesn't take into account the proven benefit of mammograms.

RICHARD WENDER: It is the most effective way we have to find breast cancer before anybody can feel it, and it's proven to reduce the risk of dying of breast cancer. So whenever we're doing decision-making, either as policymakers or as just one woman, it's important to look at both the benefits and the downsides.